TowardSpikeConformalGauge

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(\tau\right) \cosh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\tau\right) \cosh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(\sigma + \tau\right) \sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma + \tau\right) \sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)

\newcommand{\Bold}[1]{\mathbf{#1}}-1

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left(4 \, \cosh\left(\mbox{ro}\right)^{8} - 8 \, \cosh\left(\mbox{ro}\right)^{6} + 5 \, \cosh\left(\mbox{ro}\right)^{4} - \cosh\left(\mbox{ro}\right)^{2}\right)} \sin\left(\sigma\right)^{2} \cosh\left(\frac{1}{2} \, {\rm arccosh}\left(\frac{\sqrt{-\sin\left(\sigma\right) + 1} \sqrt{\sin\left(\sigma\right) + 1} {\left(2 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)}}{\sqrt{-{\left(2 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)} \sin\left(\sigma\right) + 1} \sqrt{{\left(2 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)} \sin\left(\sigma\right) + 1}}\right)\right)^{2} + {\left({\left(16 \, \cosh\left(\mbox{ro}\right)^{8} - 32 \, \cosh\left(\mbox{ro}\right)^{6} + 24 \, \cosh\left(\mbox{ro}\right)^{4} - 8 \, \cosh\left(\mbox{ro}\right)^{2} + 1\right)} \sin\left(\sigma\right)^{4} - {\left(4 \, \cosh\left(\mbox{ro}\right)^{8} - 8 \, \cosh\left(\mbox{ro}\right)^{6} + 13 \, \cosh\left(\mbox{ro}\right)^{4} - 9 \, \cosh\left(\mbox{ro}\right)^{2} + 2\right)} \sin\left(\sigma\right)^{2} + 1\right)} \sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\frac{\sqrt{-\sin\left(\sigma\right) + 1} \sqrt{\sin\left(\sigma\right) + 1} {\left(2 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)}}{\sqrt{-{\left(2 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)} \sin\left(\sigma\right) + 1} \sqrt{{\left(2 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)} \sin\left(\sigma\right) + 1}}\right)\right)^{2}}{{\left(16 \, \cosh\left(\mbox{ro}\right)^{8} - 32 \, \cosh\left(\mbox{ro}\right)^{6} + 24 \, \cosh\left(\mbox{ro}\right)^{4} - 8 \, \cosh\left(\mbox{ro}\right)^{2} + 1\right)} \sin\left(\sigma\right)^{4} - 2 \, {\left(4 \, \cosh\left(\mbox{ro}\right)^{4} - 4 \, \cosh\left(\mbox{ro}\right)^{2} + 1\right)} \sin\left(\sigma\right)^{2} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\frac{{\left(\sinh\left(\mbox{ro}\right)^{2} + \cosh\left(\mbox{ro}\right)^{2}\right)} {\left| \cos\left(\sigma\right) \right|}}{\sqrt{-4 \, \sinh\left(\mbox{ro}\right)^{2} \cosh\left(\mbox{ro}\right)^{2} + {\left(4 \, \sinh\left(\mbox{ro}\right)^{2} \cosh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma\right)^{2}}}\right)\right)^{2}

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}
-\cosh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)^{2} & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & \sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)^{2}
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-1 & \sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)^{2} \\
\sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)^{2} & \sinh\left(\frac{1}{2} \, {\rm arccosh}\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}}\right)\right)^{2} + \frac{{\left(\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}\right)} {\left(\frac{{\left(\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} + 1\right)} \tan\left(\frac{1}{2} \, \pi + \sigma\right)^{3} \cosh\left(2 \, \mbox{ro}\right)^{2}}{{\left(\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}\right)}^{2}} + \frac{-{\left(\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} + 1\right)} \tan\left(\frac{1}{2} \, \pi + \sigma\right) \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}\right)}^{2}}{4 \, {\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}} - 1\right)} {\left(\sqrt{\frac{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}{\tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} - \sinh\left(2 \, \mbox{ro}\right)^{2}}} + 1\right)} \tan\left(\frac{1}{2} \, \pi + \sigma\right)^{2} \cosh\left(2 \, \mbox{ro}\right)^{2}}
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{r_{1}^{2} \mbox{ro} \log\left(\frac{-\mbox{ro} \cos\left(\sigma\right) - \sin\left(\sigma\right)}{\cos\left(\sigma\right)}\right) - r_{1}^{2} \mbox{ro} \log\left(\frac{\mbox{ro} \cos\left(\sigma\right) + \sin\left(\sigma\right)}{\cos\left(\sigma\right)}\right) + 2 \, r_{1}^{2} \arctan\left(\frac{\sin\left(\sigma\right)}{\cos\left(\sigma\right)}\right)}{2 \, {\left(\mbox{ro}^{2} + 1\right)}}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{-r_{1}^{2} \sin\left(\sigma\right)^{2}}{\mbox{ro}^{2} \cos\left(\sigma\right)^{2} - \sin\left(\sigma\right)^{2}}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\arctan\left(\frac{a e^{\left(2 \, \sigma\right)} + 1}{\sqrt{a^{2} - 1}}\right)}{\sqrt{a^{2} - 1}}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, a e^{\left(2 \, \sigma\right)}}{{\left(\frac{{\left(a e^{\left(2 \, \sigma\right)} + 1\right)}^{2}}{a^{2} - 1} + 1\right)} {\left(a^{2} - 1\right)}}

\newcommand{\Bold}[1]{\mathbf{#1}}\sigma_{1} + \arctan\left(\frac{\sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)}{\cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}{\rm arccosh}\left(\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sigma_{1} + \arctan\left(\frac{{\left(\cosh\left(2 \, \mbox{ro}\right) - 1\right)} \tanh\left(\sigma_{2}\right)}{\sinh\left(2 \, \mbox{ro}\right)}\right) + \arctan\left(\frac{-\sinh\left(2 \, \mbox{ro}\right)}{\tanh\left(2 \, \sigma_{2}\right)}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}
-{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} + \sinh\left(\mbox{ro}\right)^{2} & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & {\left(\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} - 1\right)} {\left(\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} + 1\right)}
\end{array}\right)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_22.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Zm9yIGluIHJhbmdlKDAsNSk6"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpvVazdC/___code___.py", line 3
    for in range(_sage_const_0 ,_sage_const_5 ):
         ^
SyntaxError: invalid syntax

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-1 & 0 \\
0 & 1
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\frac{\sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)^{2}}{\cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)^{2}} + \frac{-\sinh\left(\mbox{ro}\right)}{\cosh\left(\mbox{ro}\right)}}{\frac{\sinh\left(\mbox{ro}\right)^{2} \sinh\left(\sigma_{2}\right)^{2}}{\cosh\left(\mbox{ro}\right)^{2} \cosh\left(\sigma_{2}\right)^{2}} + 1} + \frac{-{\left(\tanh\left(2 \, \sigma_{2}\right)^{2} - 1\right)} {\left(\cosh\left(2 \, \mbox{ro}\right) \cosh\left(2 \, \sigma_{2}\right) - 1\right)} \sinh\left(2 \, \mbox{ro}\right)}{{\left(\frac{\sinh\left(2 \, \mbox{ro}\right)^{2}}{\tanh\left(2 \, \sigma_{2}\right)^{2}} + 1\right)} \tanh\left(2 \, \sigma_{2}\right)^{2}}

\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} \cos\left(\sigma_{1} + \arctan\left(\frac{\sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)}{\cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} \sin\left(\sigma_{1} + \arctan\left(\frac{\sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)}{\cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} - 1} \sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} + 1} \cos\left(\sigma_{1} + \arctan\left(\frac{{\left(\cosh\left(2 \, \mbox{ro}\right) - 1\right)} \tanh\left(\sigma_{2}\right)}{\sinh\left(2 \, \mbox{ro}\right)}\right) + \arctan\left(\frac{-\sinh\left(2 \, \mbox{ro}\right)}{\tanh\left(2 \, \sigma_{2}\right)}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} - 1} \sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} + 1} \sin\left(\sigma_{1} + \arctan\left(\frac{{\left(\cosh\left(2 \, \mbox{ro}\right) - 1\right)} \tanh\left(\sigma_{2}\right)}{\sinh\left(2 \, \mbox{ro}\right)}\right) + \arctan\left(\frac{-\sinh\left(2 \, \mbox{ro}\right)}{\tanh\left(2 \, \sigma_{2}\right)}\right)\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{-\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)}{\sqrt{\sinh\left(\mbox{ro}\right)^{2} \sinh\left(\sigma_{2}\right)^{2} + \cosh\left(\mbox{ro}\right)^{2} \cosh\left(\sigma_{2}\right)^{2}}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{\sin\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)}{\sqrt{\sinh\left(\mbox{ro}\right)^{2} \sinh\left(\sigma_{2}\right)^{2} + \cosh\left(\mbox{ro}\right)^{2} \cosh\left(\sigma_{2}\right)^{2}}}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left(\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)} {\left| \sinh\left(\sigma_{2}\right) \right|}}{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2} - 1} \sinh\left(\sigma_{2}\right)}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left(\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)\right)} {\left| \sinh\left(\sigma_{2}\right) \right|}}{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2} - 1} \sinh\left(\sigma_{2}\right)}

\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)

(-sin(sigma1)*cosh(ro)*cosh(sigma2) - cos(sigma1)*sinh(ro)*sinh(sigma2), -sin(sigma1)*sinh(ro)*sinh(sigma2) + cos(sigma1)*cosh(ro)*cosh(sigma2), -sin(sigma1)*sinh(sigma2)*cosh(ro) + cos(sigma1)*sinh(ro)*cosh(sigma2), sin(sigma1)*sinh(ro)*cosh(sigma2) + cos(sigma1)*sinh(sigma2)*cosh(ro))

\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}{\left(\sin\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)\right)} {\left(\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)} - {\left(\sin\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)\right)} {\left(\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)} - {\left(\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)\right)} {\left(\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)\right)} + {\left(\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)\right)} {\left(\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)\right)}

\newcommand{\Bold}[1]{\mathbf{#1}}0

\newcommand{\Bold}[1]{\mathbf{#1}}-1

\newcommand{\Bold}[1]{\mathbf{#1}}1

0

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_84.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Tihsbig0KSk7Ck4obG4oMS80KSk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpaq3CE6/___code___.py", line 3, in <module>
    N(ln(_sage_const_4 ));
  File "free_module_element.pyx", line 2555, in sage.modules.free_module_element.FreeModuleElement_generic_dense.__call__ (sage/modules/free_module_element.c:17127)
  File "expression.pyx", line 3426, in sage.symbolic.expression.Expression.__call__ (sage/symbolic/expression.cpp:15476)
  File "ring.pyx", line 638, in sage.symbolic.ring.SymbolicRing._call_element_ (sage/symbolic/ring.cpp:6460)
ValueError: the number of arguments must be less than or equal to 0

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_86.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cGxvdChzaW5oKDEpL3RhbmgoMip1KSwgKHUsMSwzKSk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmp1WAgB2/___code___.py", line 3, in <module>
    exec compile(u'plot(sinh(_sage_const_1 )/tanh(_sage_const_2 *u), (u,_sage_const_1 ,_sage_const_3 ))
  File "", line 1, in <module>
    
NameError: name 'u' is not defined

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_87.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cGxvdChhcmN0YW4oc2luaCgxKS90YW5oKDIqdSkpLCAodSwtMiwyKSk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpk6NsNd/___code___.py", line 3, in <module>
    exec compile(u'plot(arctan(sinh(_sage_const_1 )/tanh(_sage_const_2 *u)), (u,-_sage_const_2 ,_sage_const_2 ))
  File "", line 1, in <module>
    
NameError: name 'u' is not defined

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_88.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cGxvdChhcmN0YW4odSksKC0xMDAsMTAwKSk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpMHyhP0/___code___.py", line 3, in <module>
    exec compile(u'plot(arctan(u),(-_sage_const_100 ,_sage_const_100 ))
  File "", line 1, in <module>
    
NameError: name 'u' is not defined

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_90.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("PGgzIHN0eWxlPSJjb2xvcjogIzgwMDA4MDsiPkludGVudGVtb3MgcmVzcGV0aXIgbGFzIGN1ZW50YXMgZW4gZWwgY2FzbyBjb29yZGVuYWRhcyB3b3JsZHNoZWV0IHogKG1ldHJpY2EgaW5kdWNpZGEgZXVjbGlkZWEpIDwvaDM+"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpcmku9g/___code___.py", line 2
    <h3 style="color: #800080;">Intentemos respetir las cuentas en el caso coordenadas worldsheet z (metrica inducida euclidea) </h3>
    ^
SyntaxError: invalid syntax

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_92.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("SWUxPSBpbnRlZ3JhbCgxLyhhKmNvcygyKnNpZykrMSksIHNpZyk7IEllMQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpQfWS49/___code___.py", line 3, in <module>
    exec compile(u'Ie1= integral(_sage_const_1 /(a*cos(_sage_const_2 *sig)+_sage_const_1 ), sig); Ie1
  File "", line 1, in <module>
    
NameError: name 'a' is not defined

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_93.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("KGxvZygoKGEgLSAxKSpzaW4oMipzaWdtYSkvKGNvcygyKnNpZ21hKSArIDEpIC0gc3FydChhXjIgLSAxKSkvKChhIC0KMSkqc2luKDIqc2lnbWEpLyhjb3MoMipzaWdtYSkgKyAxKSArIHNxcnQoYV4yIC0gMSkpKSkuc2ltcGxpZnlfZnVsbCgpLnNob3coKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpxT2arr/___code___.py", line 3, in <module>
    (log(((a - _sage_const_1 )*sin(_sage_const_2 *sigma)/(cos(_sage_const_2 *sigma) + _sage_const_1 ) - sqrt(a**_sage_const_2  - _sage_const_1 ))/((a -
NameError: name 'a' is not defined

\newcommand{\Bold}[1]{\mathbf{#1}}\sigma_{1} - \frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right) + \frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}{\rm arccosh}\left(\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sigma_{1} - \frac{1}{2} \, \log\left(\frac{-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) - \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)}{\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)}\right) + \arctan\left(\frac{-i \, \sinh\left(2 \, \mbox{ro}\right)}{\tan\left(2 \, \sigma_{2}\right)}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}
-{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} + \sinh\left(\mbox{ro}\right)^{2} & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & {\left(\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} - 1\right)} {\left(\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cosh\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} + 1\right)}
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-1 & \frac{\left(i + 1\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + {\left(4 \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + 4 \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\sigma_{2}\right)^{4} + \left(i + 1\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) - {\left(\left(2 i + 4\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + \left(i + 4\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\sigma_{2}\right)^{2} - {\left(\left(-2 i\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + \left(-3 i\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + {\left(\left(4 i\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + \left(4 i\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + i \, \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\sigma_{2}\right)^{2} - i \, \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sinh\left(\sigma_{2}\right)^{2}}{\sin\left(\sigma_{2}\right)^{6} \sinh\left(\mbox{ro}\right)^{4} \cosh\left(\mbox{ro}\right)^{2} - \cos\left(\sigma_{2}\right)^{6} \sinh\left(\mbox{ro}\right)^{2} \cosh\left(\mbox{ro}\right)^{4} - {\left(2 \, \sinh\left(\mbox{ro}\right)^{4} \cosh\left(\mbox{ro}\right)^{2} + {\left(\cosh\left(\mbox{ro}\right)^{4} + 1\right)} \sinh\left(\mbox{ro}\right)^{2}\right)} \sin\left(\sigma_{2}\right)^{4} \cos\left(\sigma_{2}\right)^{2} + {\left(\sinh\left(\mbox{ro}\right)^{4} \cosh\left(\mbox{ro}\right)^{2} + 2 \, \sinh\left(\mbox{ro}\right)^{2} \cosh\left(\mbox{ro}\right)^{4} + \cosh\left(\mbox{ro}\right)^{2}\right)} \sin\left(\sigma_{2}\right)^{2} \cos\left(\sigma_{2}\right)^{4}} \\
\frac{\left(i + 1\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + {\left(4 \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + 4 \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\sigma_{2}\right)^{4} + \left(i + 1\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) - {\left(\left(2 i + 4\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + \left(i + 4\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\sigma_{2}\right)^{2} - {\left(\left(-2 i\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + \left(-3 i\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + {\left(\left(4 i\right) \, \sinh\left(\mbox{ro}\right)^{5} \cosh\left(\mbox{ro}\right) + \left(4 i\right) \, \sinh\left(\mbox{ro}\right)^{3} \cosh\left(\mbox{ro}\right) + i \, \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\sigma_{2}\right)^{2} - i \, \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sinh\left(\sigma_{2}\right)^{2}}{\sin\left(\sigma_{2}\right)^{6} \sinh\left(\mbox{ro}\right)^{4} \cosh\left(\mbox{ro}\right)^{2} - \cos\left(\sigma_{2}\right)^{6} \sinh\left(\mbox{ro}\right)^{2} \cosh\left(\mbox{ro}\right)^{4} - {\left(2 \, \sinh\left(\mbox{ro}\right)^{4} \cosh\left(\mbox{ro}\right)^{2} + {\left(\cosh\left(\mbox{ro}\right)^{4} + 1\right)} \sinh\left(\mbox{ro}\right)^{2}\right)} \sin\left(\sigma_{2}\right)^{4} \cos\left(\sigma_{2}\right)^{2} + {\left(\sinh\left(\mbox{ro}\right)^{4} \cosh\left(\mbox{ro}\right)^{2} + 2 \, \sinh\left(\mbox{ro}\right)^{2} \cosh\left(\mbox{ro}\right)^{4} + \cosh\left(\mbox{ro}\right)^{2}\right)} \sin\left(\sigma_{2}\right)^{2} \cos\left(\sigma_{2}\right)^{4}} & \frac{-{\left(256 \, \cosh\left(\mbox{ro}\right)^{16} - 1024 \, \cosh\left(\mbox{ro}\right)^{14} + 1792 \, \cosh\left(\mbox{ro}\right)^{12} - 1792 \, \cosh\left(\mbox{ro}\right)^{10} + 1120 \, \cosh\left(\mbox{ro}\right)^{8} - 448 \, \cosh\left(\mbox{ro}\right)^{6} + 112 \, \cosh\left(\mbox{ro}\right)^{4} - 16 \, \cosh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{16} + \left(2 i + 1\right) \, \cosh\left(\mbox{ro}\right)^{16} - {\left(1024 \, \cosh\left(\mbox{ro}\right)^{16} - 4224 \, \cosh\left(\mbox{ro}\right)^{14} + 7616 \, \cosh\left(\mbox{ro}\right)^{12} - 7840 \, \cosh\left(\mbox{ro}\right)^{10} + 5040 \, \cosh\left(\mbox{ro}\right)^{8} - 2072 \, \cosh\left(\mbox{ro}\right)^{6} + 532 \, \cosh\left(\mbox{ro}\right)^{4} - 78 \, \cosh\left(\mbox{ro}\right)^{2} + 5\right)} \cos\left(\sigma_{2}\right)^{14} + \left(-8 i - 5\right) \, \cosh\left(\mbox{ro}\right)^{14} + {\left(1792 \, \cosh\left(\mbox{ro}\right)^{16} - 7616 \, \cosh\left(\mbox{ro}\right)^{14} + 14080 \, \cosh\left(\mbox{ro}\right)^{12} - 14800 \, \cosh\left(\mbox{ro}\right)^{10} + 9680 \, \cosh\left(\mbox{ro}\right)^{8} - 4036 \, \cosh\left(\mbox{ro}\right)^{6} + 1048 \, \cosh\left(\mbox{ro}\right)^{4} - 155 \, \cosh\left(\mbox{ro}\right)^{2} + 10\right)} \cos\left(\sigma_{2}\right)^{12} + \left(12 i + 10\right) \, \cosh\left(\mbox{ro}\right)^{12} + {\left(\left(-64 i - 1792\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(224 i + 7808\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(-320 i - 14688\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(240 i + 15600\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(-100 i - 10240\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(22 i + 4256\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(-2 i - 1094\right) \, \cosh\left(\mbox{ro}\right)^{4} + 159 \, \cosh\left(\mbox{ro}\right)^{2} - 10\right)} \cos\left(\sigma_{2}\right)^{10} + \left(-8 i - 10\right) \, \cosh\left(\mbox{ro}\right)^{10} + {\left(\left(160 i + 1120\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(-576 i - 4976\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(848 i + 9440\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(-656 i - 9992\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(282 i + 6454\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(-64 i - 2603\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(6 i + 639\right) \, \cosh\left(\mbox{ro}\right)^{4} - 87 \, \cosh\left(\mbox{ro}\right)^{2} + 5\right)} \cos\left(\sigma_{2}\right)^{8} + \left(2 i + 5\right) \, \cosh\left(\mbox{ro}\right)^{8} + {\left(\left(-160 i - 448\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(592 i + 2024\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(-888 i - 3844\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(692 i + 3994\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(-296 i - 2471\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(66 i + 925\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(-6 i - 202\right) \, \cosh\left(\mbox{ro}\right)^{4} + 23 \, \cosh\left(\mbox{ro}\right)^{2} - 1\right)} \cos\left(\sigma_{2}\right)^{6} - \cosh\left(\mbox{ro}\right)^{6} + {\left(\left(80 i + 112\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(-304 i - 516\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(460 i + 980\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(-352 i - 989\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(142 i + 569\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(-28 i - 185\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(2 i + 31\right) \, \cosh\left(\mbox{ro}\right)^{4} - 2 \, \cosh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{4} + {\left(\left(-20 i - 16\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(78 i + 76\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(-118 i - 146\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(86 i + 144\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(-30 i - 76\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(4 i + 20\right) \, \cosh\left(\mbox{ro}\right)^{6} - 2 \, \cosh\left(\mbox{ro}\right)^{4}\right)} \cos\left(\sigma_{2}\right)^{2} + {\left(\left(-4 i\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(18 i + 2\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(-32 i - 9\right) \, \cosh\left(\mbox{ro}\right)^{12} + {\left(\left(128 i\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(-512 i\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(864 i\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(-800 i\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(440 i\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(-144 i\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(26 i\right) \, \cosh\left(\mbox{ro}\right)^{4} + \left(-2 i\right) \, \cosh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{10} + \left(28 i + 16\right) \, \cosh\left(\mbox{ro}\right)^{10} + {\left(\left(-320 i\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(1312 i + 32\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(-2272 i - 112\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(2160 i + 160\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(-1220 i - 120\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(410 i + 50\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(-76 i - 11\right) \, \cosh\left(\mbox{ro}\right)^{4} + \left(6 i + 1\right) \, \cosh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{8} + \left(-12 i - 14\right) \, \cosh\left(\mbox{ro}\right)^{8} + {\left(\left(320 i\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(-1344 i - 64\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(2368 i + 240\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(-2272 i - 368\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(1284 i + 296\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(-428 i - 132\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(78 i + 31\right) \, \cosh\left(\mbox{ro}\right)^{4} + \left(-6 i - 3\right) \, \cosh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{6} + \left(2 i + 6\right) \, \cosh\left(\mbox{ro}\right)^{6} + {\left(\left(-160 i\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(688 i + 48\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(-1224 i - 192\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(1164 i + 312\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(-636 i - 264\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(198 i + 123\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(-32 i - 30\right) \, \cosh\left(\mbox{ro}\right)^{4} + \left(2 i + 3\right) \, \cosh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{4} - \cosh\left(\mbox{ro}\right)^{4} + {\left(\left(40 i\right) \, \cosh\left(\mbox{ro}\right)^{16} + \left(-176 i - 16\right) \, \cosh\left(\mbox{ro}\right)^{14} + \left(314 i + 68\right) \, \cosh\left(\mbox{ro}\right)^{12} + \left(-290 i - 116\right) \, \cosh\left(\mbox{ro}\right)^{10} + \left(146 i + 101\right) \, \cosh\left(\mbox{ro}\right)^{8} + \left(-38 i - 47\right) \, \cosh\left(\mbox{ro}\right)^{6} + \left(4 i + 11\right) \, \cosh\left(\mbox{ro}\right)^{4} - \cosh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{2}\right)} \cosh\left(\sigma_{2}\right)^{2}}{{\left(256 \, \sinh\left(\mbox{ro}\right)^{16} + 1024 \, \sinh\left(\mbox{ro}\right)^{14} + 1792 \, \sinh\left(\mbox{ro}\right)^{12} + 1792 \, \sinh\left(\mbox{ro}\right)^{10} + 1120 \, \sinh\left(\mbox{ro}\right)^{8} + 448 \, \sinh\left(\mbox{ro}\right)^{6} + 112 \, \sinh\left(\mbox{ro}\right)^{4} + 16 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{16} + \sinh\left(\mbox{ro}\right)^{16} - {\left(1024 \, \sinh\left(\mbox{ro}\right)^{16} + 3968 \, \sinh\left(\mbox{ro}\right)^{14} + 6720 \, \sinh\left(\mbox{ro}\right)^{12} + 6496 \, \sinh\left(\mbox{ro}\right)^{10} + 3920 \, \sinh\left(\mbox{ro}\right)^{8} + 1512 \, \sinh\left(\mbox{ro}\right)^{6} + 364 \, \sinh\left(\mbox{ro}\right)^{4} + 50 \, \sinh\left(\mbox{ro}\right)^{2} + 3\right)} \cos\left(\sigma_{2}\right)^{14} + 3 \, \sinh\left(\mbox{ro}\right)^{14} + {\left(1792 \, \sinh\left(\mbox{ro}\right)^{16} + 6720 \, \sinh\left(\mbox{ro}\right)^{14} + 10944 \, \sinh\left(\mbox{ro}\right)^{12} + 10096 \, \sinh\left(\mbox{ro}\right)^{10} + 5760 \, \sinh\left(\mbox{ro}\right)^{8} + 2076 \, \sinh\left(\mbox{ro}\right)^{6} + 460 \, \sinh\left(\mbox{ro}\right)^{4} + 57 \, \sinh\left(\mbox{ro}\right)^{2} + 3\right)} \cos\left(\sigma_{2}\right)^{12} + 3 \, \sinh\left(\mbox{ro}\right)^{12} - {\left(1792 \, \sinh\left(\mbox{ro}\right)^{16} + 6496 \, \sinh\left(\mbox{ro}\right)^{14} + 10096 \, \sinh\left(\mbox{ro}\right)^{12} + 8752 \, \sinh\left(\mbox{ro}\right)^{10} + 4600 \, \sinh\left(\mbox{ro}\right)^{8} + 1486 \, \sinh\left(\mbox{ro}\right)^{6} + 283 \, \sinh\left(\mbox{ro}\right)^{4} + 28 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{10} + \sinh\left(\mbox{ro}\right)^{10} + 5 \, {\left(224 \, \sinh\left(\mbox{ro}\right)^{16} + 784 \, \sinh\left(\mbox{ro}\right)^{14} + 1152 \, \sinh\left(\mbox{ro}\right)^{12} + 920 \, \sinh\left(\mbox{ro}\right)^{10} + 430 \, \sinh\left(\mbox{ro}\right)^{8} + 117 \, \sinh\left(\mbox{ro}\right)^{6} + 17 \, \sinh\left(\mbox{ro}\right)^{4} + \sinh\left(\mbox{ro}\right)^{2}\right)} \cos\left(\sigma_{2}\right)^{8} - {\left(448 \, \sinh\left(\mbox{ro}\right)^{16} + 1512 \, \sinh\left(\mbox{ro}\right)^{14} + 2076 \, \sinh\left(\mbox{ro}\right)^{12} + 1486 \, \sinh\left(\mbox{ro}\right)^{10} + 585 \, \sinh\left(\mbox{ro}\right)^{8} + 120 \, \sinh\left(\mbox{ro}\right)^{6} + 10 \, \sinh\left(\mbox{ro}\right)^{4}\right)} \cos\left(\sigma_{2}\right)^{6} + {\left(112 \, \sinh\left(\mbox{ro}\right)^{16} + 364 \, \sinh\left(\mbox{ro}\right)^{14} + 460 \, \sinh\left(\mbox{ro}\right)^{12} + 283 \, \sinh\left(\mbox{ro}\right)^{10} + 85 \, \sinh\left(\mbox{ro}\right)^{8} + 10 \, \sinh\left(\mbox{ro}\right)^{6}\right)} \cos\left(\sigma_{2}\right)^{4} - {\left(16 \, \sinh\left(\mbox{ro}\right)^{16} + 50 \, \sinh\left(\mbox{ro}\right)^{14} + 57 \, \sinh\left(\mbox{ro}\right)^{12} + 28 \, \sinh\left(\mbox{ro}\right)^{10} + 5 \, \sinh\left(\mbox{ro}\right)^{8}\right)} \cos\left(\sigma_{2}\right)^{2}}
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} \cos\left(\sigma_{1} - \frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right) + \frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} \sin\left(\sigma_{1} - \frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right) + \frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} - 1} \sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} + 1} \cos\left(\sigma_{1} - \frac{1}{2} \, \log\left(\frac{-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) - \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)}{\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)}\right) + \arctan\left(\frac{-i \, \sinh\left(2 \, \mbox{ro}\right)}{\tan\left(2 \, \sigma_{2}\right)}\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} - 1} \sqrt{\sqrt{{\left(2 \, \sinh\left(\mbox{ro}\right)^{2} + 1\right)} \cos\left(\sigma_{2}\right)^{2} - \sinh\left(\mbox{ro}\right)^{2}} + 1} \sin\left(\sigma_{1} - \frac{1}{2} \, \log\left(\frac{-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) - \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)}{\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)}\right) + \arctan\left(\frac{-i \, \sinh\left(2 \, \mbox{ro}\right)}{\tan\left(2 \, \sigma_{2}\right)}\right)\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(\sigma_{1} - \frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right) + \frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1} - \frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right) + \frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{{\left({\left(\left(2 i\right) \, \cos\left(\sigma_{1}\right) \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) - \sin\left(\sigma_{1}\right) \sin\left(\sigma_{2}\right) \cos\left(\sigma_{2}\right) - i \, \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \cos\left(\frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right) + {\left(\left(2 i\right) \, \sin\left(\sigma_{1}\right) \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) - i \, \sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) + \sin\left(\sigma_{2}\right) \cos\left(\sigma_{1}\right) \cos\left(\sigma_{2}\right)\right)} \sin\left(\frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)\right)} \sin\left(\frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right) + {\left({\left(\left(-2 i\right) \, \cos\left(\sigma_{1}\right) \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) + \sin\left(\sigma_{1}\right) \sin\left(\sigma_{2}\right) \cos\left(\sigma_{2}\right) + i \, \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)\right)} \sin\left(\frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right) + {\left(\left(2 i\right) \, \sin\left(\sigma_{1}\right) \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) - i \, \sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) + \sin\left(\sigma_{2}\right) \cos\left(\sigma_{1}\right) \cos\left(\sigma_{2}\right)\right)} \cos\left(\frac{1}{2} \, \log\left(-\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)\right)} \cos\left(\frac{1}{2} \, \log\left(\sin\left(\sigma_{2}\right) \sinh\left(\mbox{ro}\right) + \cos\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)\right)\right)}{\sqrt{-2 \, \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) + \sin\left(\sigma_{2}\right) \cos\left(\sigma_{2}\right) + \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)} \sqrt{2 \, \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right) + \sin\left(\sigma_{2}\right) \cos\left(\sigma_{2}\right) - \sinh\left(\mbox{ro}\right) \cosh\left(\mbox{ro}\right)}}

(-sqrt((2*sinh(ro)^2 + 1)*cos(sigma2)^2 - sinh(ro)^2)*sin(sigma1 - 1/2*log(-sin(sigma2)*sinh(ro) + cos(sigma2)*cosh(ro)) + 1/2*log(sin(sigma2)*sinh(ro) + cos(sigma2)*cosh(ro))), sqrt((2*sinh(ro)^2 + 1)*cos(sigma2)^2 - sinh(ro)^2)*cos(sigma1 - 1/2*log(-sin(sigma2)*sinh(ro) + cos(sigma2)*cosh(ro)) + 1/2*log(sin(sigma2)*sinh(ro) + cos(sigma2)*cosh(ro))), -sqrt(sqrt((2*sinh(ro)^2 + 1)*cos(sigma2)^2 - sinh(ro)^2) - 1)*sqrt(sqrt((2*sinh(ro)^2 + 1)*cos(sigma2)^2 - sinh(ro)^2) + 1)*sin(sigma1 - 1/2*log(-(sin(sigma2)*sinh(ro) - cos(sigma2)*cosh(ro))/(sin(sigma2)*sinh(ro) + cos(sigma2)*cosh(ro))) + arctan(-I*sinh(2*ro)/tan(2*sigma2))), sqrt(sqrt((2*sinh(ro)^2 + 1)*cos(sigma2)^2 - sinh(ro)^2) - 1)*sqrt(sqrt((2*sinh(ro)^2 + 1)*cos(sigma2)^2 - sinh(ro)^2) + 1)*cos(sigma1 - 1/2*log(-(sin(sigma2)*sinh(ro) - cos(sigma2)*cosh(ro))/(sin(sigma2)*sinh(ro) + cos(sigma2)*cosh(ro))) + arctan(-I*sinh(2*ro)/tan(2*sigma2))))

(((4*I + 4)*cosh(ro)^5 + (-4*I - 4)*cosh(ro)^3 + (I + 1)*cosh(ro))*cos(sigma2)^4*sinh(ro) + ((-4*I - 4)*cosh(ro)^5 + (4*I + 4)*cosh(ro)^3 + (-I - 1)*cosh(ro))*cos(sigma2)^2*sinh(ro) + ((I + 1)*cosh(ro)^5 + (-I - 1)*cosh(ro)^3)*sinh(ro))/(sin(sigma2)^6*sinh(ro)^4*cosh(ro)^2 - cos(sigma2)^6*sinh(ro)^2*cosh(ro)^4 - (2*sinh(ro)^4*cosh(ro)^2 + (cosh(ro)^4 + 1)*sinh(ro)^2)*sin(sigma2)^4*cos(sigma2)^2 + (sinh(ro)^4*cosh(ro)^2 + 2*sinh(ro)^2*cosh(ro)^4 + cosh(ro)^2)*sin(sigma2)^2*cos(sigma2)^4)

\newcommand{\Bold}[1]{\mathbf{#1}}{\left(\left(4 i + 4\right) \, \cosh\left(\mbox{ro}\right)^{5} + \left(-4 i + 4\right) \, \cosh\left(\mbox{ro}\right)^{3} + \left(i + 1\right) \, \cosh\left(\mbox{ro}\right)\right)} \cos\left(\sigma_{2}\right)^{4} \sinh\left(\mbox{ro}\right) + {\left(\left(-4 i + 4\right) \, \cosh\left(\mbox{ro}\right)^{5} + \left(4 i + 4\right) \, \cosh\left(\mbox{ro}\right)^{3} + \left(-i + 1\right) \, \cosh\left(\mbox{ro}\right)\right)} \cos\left(\sigma_{2}\right)^{2} \sinh\left(\mbox{ro}\right) + {\left(\left(i + 1\right) \, \cosh\left(\mbox{ro}\right)^{5} + \left(-i + 1\right) \, \cosh\left(\mbox{ro}\right)^{3}\right)} \sinh\left(\mbox{ro}\right)

__main__:3: DeprecationWarning: Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)
-1

\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) + \sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) - \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \cosh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \sinh\left(\sigma_{2}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\sin\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right) - \cos\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right)

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a2*b3*c4 - a2*b4*c3 - a3*b2*c4 + a3*b4*c2 + a4*b2*c3 - a4*b3*c2

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1

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, \sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) + \frac{1}{2} \, \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{2} \, \sin\left(\sigma_{1}\right) \sinh\left(\mbox{ro}\right) \cosh\left(\sigma_{2}\right) - \frac{1}{2} \, \cos\left(\sigma_{1}\right) \sinh\left(\sigma_{2}\right) \cosh\left(\mbox{ro}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{4}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{4}